How do you identify the oblique asymptote of f(x) = (x^2+6x-9)/(x-2)?

May 2, 2018

Below

Explanation:

$f \left(x\right) = \frac{{x}^{2} + 6 x - 9}{x - 2}$

$f \left(x\right) = \frac{\left(x - 2\right) \left(x + 8\right) + 7}{x - 2}$

$f \left(x\right) = \left(x + 8\right) + \frac{7}{x - 2}$

Therefore, the oblique asymptote is $y = x + 8$ and the vertical asymptote is $x = 2$

graph{(x^2+6x-9)/(x-2) [-10, 10, -5, 5]}